Back to: Algebra 1

An **inequality** is a mathematical relationship between two expressions and is represented using one of the following symbols:

≤: “less than or equal to,”

<: “less than,”

>: “greater than,”

≥: “greater than or equal to.”

Note: Pay close attention to phrases such as “at most” (≤) or “at least” (≥).

**Example**: The sum of 8y and 3y is greater than 66.

In symbols, 11y > 66

y > 6 Therefore y cannot be 6, it must be greater than 6.

**Example**: The sum of a number and 5 is at most 23.

In symbols, n + 5 ≤ 23 *“At most” means less than or equal to.*

n ≤ 19

**Example**: The weight of the truck w, plus its load of two thousand pounds must be at least four thousand pounds.

In symbol, w + 2000 ≥ 4000 *“At least” means greater than or equal to.*

w ≥ 2000

**Example**: Solve the inequality,

27 < x – 3

+3 +3

———————

30 < x

**Example**: Solve the equation,

– 10 + x > 30

+10 +10

——————-

x > 40